Large N gauge theory — Expansions and transitions

Douglas, Michael R.

doi:10.1016/0920-5632(95)00431-8

Cited by 31 publications

(28 citation statements)

References 56 publications

(120 reference statements)

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“…Note that ordinary two-dimensional Yang-Mills theory at large N exhibits exactly an e α √ E rise in its density of states [33]. The realization of the noncommutative gauge theory as a particular kind of large N limit of commutative gauge theory thereby supports the general validity of (3.15).…”

Section: The Spectrum Of Noncommutative Instantonssupporting

confidence: 56%

Instantons, fluxons, and open gauge string theory

Seminara¹,

Szabo²

2005

Advances in Theoretical and Mathematical Physics

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Abstract:We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification limit of noncommutative torus instantons is shown to map in a very precise way, at both the classical and quantum level, onto fluxon solutions on the noncommutative plane. The weak-coupling singularities of the usual Gross-Taylor string partition function for QCD on the torus are studied in the instanton representation and its double scaling limit, appropriate for the mapping onto noncommutative gauge theory, is shown to be a generating function for the volumes of the principal moduli spaces of holomorphic differentials. The noncommutative deformation of this moduli space geometry is described and appropriate open string interpretations are proposed in terms of the fluxon expansion.

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Section: The Spectrum Of Noncommutative Instantonssupporting

confidence: 56%

Instantons, fluxons, and open gauge string theory

Seminara¹,

Szabo²

2005

Advances in Theoretical and Mathematical Physics

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“…Some aspects of Y M 2 are also reviewed in [120,18,21,97,71]. Cohomological field theory is also reviewed in [205,229,34].…”

Section: Some Related Reviewsmentioning

confidence: 99%

Lectures on 2D yang-mills theory, equivariant cohomology and topological field theories

Cordes

Moore

Ramgoolam

1995

Nuclear Physics B - Proceedings Supplements

313

597

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These are expository lectures reviewing (1) recent developments in two-dimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinite-dimensional differential geometry.We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.

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“…The strong coupling expansion of the lattice gauge theories and topological classification of the QCD diagrams, together with the last progress in solving two-dimensional QCD, put forward the ultimate conjunction that QCD is exactly equivalent to a string theory [1]. One can also expect a new progress in understanding of the QCD string in four dimensions [2,3]. In this approach one should derive the relevant string theory directly from properly regularized QCD path integrals.…”

Section: String With Linear Actionmentioning

confidence: 99%

“…and α i,j is the angle between two neighbor faces of M having a common edge < i, j > of the length λ i,j . The regularized string (1), (2) is well defined in any dimensions and for arbitrary topology of the surface M.…”

Section: String With Linear Actionmentioning

confidence: 99%

“…In a recent paper [9] two of the authors have introduced a spin statistical system on the lattice, the low temperature expansion of which generates random surfaces with linear action A(M) (2). In this lattice implementation of the linear string the corresponding Hamiltonian depends on the way how we ascribe the weights on the self-intersection edges.…”

Section: Surfaces On the Latticementioning

confidence: 99%

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Geometrical string and dual spin systems

Savvidy

Wegner

1995

Nuclear Physics B

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We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge Hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual Hamiltonian represents a new type of spin system with local gauge invariance. At each vertex ξ there are d(d − 1)/2 Ising spins Λ µ,ν = Λ ν,µ , µ = ν = 1, .., d and one Ising spin Γ on every link (ξ, ξ+e µ ). For the frozen spin Γ ≡ 1 the dual Hamiltonian factorizes into d(d − 1)/2 two-dimensional Ising ferromagnets and into antiferromagnets in the case Γ ≡ −1. For fluctuating Γ it is a sort of spin glass system with local gauge invariance. The generalization to p-branes is given.

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Large N gauge theory — Expansions and transitions

Cited by 31 publications

References 56 publications

Instantons, fluxons, and open gauge string theory

Instantons, fluxons, and open gauge string theory

Lectures on 2D yang-mills theory, equivariant cohomology and topological field theories

Geometrical string and dual spin systems

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